I can totally understand your frustration since podPress is a complex plugin and in some cases not very user-friendly. But reinstalling WP or a plugin is helping only in few cases.
Your problems, especially the one with the feed, looked more like a cache problem to me until I visited your site some minutes ago.
Now that I watched your site and looked into the source code of your front page, I discovered that you have switched on the statistic feature of podPress while using the default permalink structure of WP.
That is the reason why the player says "file not found". The player is actually not able to find the file because when you are using the statistic feature, podPress rewrites and tries to redirect (in a reversible manner) the links of the media files. That is necessary to count the how many times a file has been played and downloaded. But this will only work if you switch at least to the "Day and name" structure (and if you are using the podPress stat logging "Use WP permalinks", which is the stats method that I would recommend).
That is probably the same reason why your feed is not valid.
The function which creates the feed adds only posts to the ?feed=podcast - feed if the posts containing media files. But if something is wrong with the media file URLs then feed is empty and not valid.
If you install podPress in a fresh WP installation then you need to save the permalink settings of the blog again after you have activated podPress. Because WP writes these permalink rules (most times) into a file with the name .htaccess. podPress adds feeds to your blog like the feed with the name podcast as long as it is active. But these feeds are not automatically part of these rules in the .htaccess file, so WP needs to rewrite the rules.
Please, control whether there is such a .htaccess file in the root directory (the one where the wp-config.php file is) of your blog after you have activated the "Day and name" permalinks.
Please, test the stats support on the general settings page of podPress afterwards. If it says "Test: Failed" then something is still wrong with this .htaccess file (maybe it is not in place or not writeable) and the stats feature will not work.
Use "Counts Only" or "Full" as the stats method. But keep in mind that the "Counts only" method counts also while you are using "Full", but not vice versa. Since 8.8.5 the tables and graph will show the result of "Counts Only" OR "Full/Full+". (Full+ is practically the same as Full. It logs the same values to the same data base table.)
podPress and the support:
Dan, the main author of the plugin, seems to be very busy with other things. But at the moment there is some support of the WP community as you can read e.g. in the long threads here: http://wordpress.org/tags/podpress?forum_id=10.
But I hope that Dan continues the development of this plugin or that there will be some other people (more than one) out there who like do that, too.
At the moment I have write permissions for the podPress folders in the repository, too and I can write patches for it. If you notice errors/bugs then please, write a post like you have in the last days and describe the circumstances in much details as you can. Or ask simply your questions. But I want to remind you that figuring out the cause of a problem in a foreign blog is sometimes not easy.